Method and system for processing measurement signals to obtain a value for physical parameter

ABSTRACT

In a measurement system wherein time-varying physical signals containing frequency information related to a physical parameter of an object are measured to obtain corresponding time-varying measurement signals, a method and system are disclosed for processing the measurement signals to obtain a value for the physical parameter by first extracting the frequency information from the measurement signals. The frequency information includes at least one desired frequency and its amplitude and decay rate. Then, the frequency information is converted to a value for the physical parameter. The measurement signals are discrete time ultrasonic signals. Extraction is performed by transforming the ultrasonic signals to a Z-domain and converting at least one zero or pole in the Z-domain to the at least one frequency and its decay rate.

This is a divisional of copending application Ser. No. 09/620,496 filedon Jul. 20, 2000 which is a divisional of application Ser. No.08/952,555, filed Nov. 21, 1997, issued U.S. Pat. No. 6,092,419, and thebenefit of provisional applications Nos. 60/031,717; 60/032,006, bothfiled Nov. 22, 1996.

TECHNICAL FIELD

This invention relates to methods and systems for processing measurementsignals to obtain a value for a physical parameter and, in particular,to methods and systems for processing measurement signals to obtain avalue for a physical parameter of an object wherein the measurementsignals are obtained by measuring time-varying physical signalscontaining frequency information related to the physical parameter ofthe object.

BACKGROUND ART

In any coating process of an article of manufacture such as anautomotive body, there is an optimum specification for the resultingfilm build, i.e., thickness of the resulting coating layer involvingacceptable performance, appearance and materials cost. The ability tomeasure this film build on-line in a production environment would bebeneficial to the manufacturer.

Often, any method for measuring the film build of a coating layer mustrequire that no contact with the film occur either to avoid degradingthe effectiveness or marring the appearance of the film. This isespecially true for coatings while they are wet.

With manufacturing film build data, the bulk materials costs can becontrolled by applying the minimum amount of material to reach anacceptable film build. Other savings can also be realized, for examplemeasuring and improving the transfer efficiency of the coating processand correlating film build to the quality of the appearance of the finalcoated surface. An example process and production environment that wouldbenefit from the ability to measure film build on-line is the paintingof automobile bodies.

In automated painting operations, a prime concern is the reduction ofenvironmental impacts due to the evaporation of solvents. Means ofreducing the amount of solvent released into the atmosphere includeelectrostatic application of the paint and the use of waterborne paints.Electrostatic application increases the quantity of paint delivered tothe painted object, and thus reduces the total quantity of paintrequired due to the decrease in overspray. The use of waterborne paintsdramatically reduces the quantity of solvent utilized in the paintbecause water is used as a vehicle for paint delivery rather thansolvent. Environmental concerns may dictate the exclusive use ofwaterborne paints in the future.

In order to further reduce waste, thus reducing solvent emissions, andto improve the quality of the finished painted article, it may benecessary to monitor or sense various paint physical parameters such asthickness with precision to effect control.

Waterborne paints are electrically conductive and, therefore, must beisolated from the environment such that an electrostatic charge may beimparted to the flow of paint. This isolation must be at least 100kiloVolts. Further, the painting environment is a hazardous environmentdue to the few remaining solvents in the paint. Therefore, any devicewhich meters or measures the physical parameters of paint must provideelectrostatic isolation and limit energies within the paintingenvironment to less than that required for ignition.

The painting process for automobiles involves applying several coatingsof different materials to an underlying metal or plastic substrate 10.As illustrated in FIG. 1, these coatings may include variousanti-corrosion layers such as a phosphate layer 12, an E-coat layer 14,primer layer(s) 16, colored paint layers 18 (referred to as base coats),and a transparent protective and appearance improving material(s) calleda clearcoat 20. The ability to measure both total film build, i.e., thetotal thickness of all layers, of the thickness of each individuallayer, in both the wet or dry states would be useful.

One non-contact method for measuring solid film thickness and/or otherphysical properties of the film is provided by ultrasound generation inthe film and subsequent ultrasound detection. However, this methodtypically locally damages or destroys the film.

For example, U.S. Pat. No. 4,659,224 discloses optical interferometricreception of ultrasound energy using a confocal Fabry-Perotinterferometer and the detection of the Doppler shift of the laser linefrequency as the method to detect the ultrasound.

U.S. Pat. No. 5,137,361 discloses optical detection of a surface motionof an object using a stabilized interferometric cavity. Theinterferometer cavity is stabilized by controlling the position of therear cavity mirror with a piezoelectric pusher.

U.S. Pat. No. 5,402,235 discloses imaging of ultrasonic-surface motionby optical multiplexing. Ultrasound is detected using an array ofdetectors and a “demodulator”. The demodulator is typically aphoto-refractive crystal within which a hologram of the laser beam, bothdirectly from the laser and reflected off the sample's surface, aresimultaneously written. The interference between sample laser beam andthe beam reflected off the sample surface takes place between the twoholographic images generated within the crystal.

U.S. Pat. No. 5,590,090 discloses an ultrasonic detector using verticalcavity surface emitting lasers. The method requires contact between thesample and the equipment.

U.S. Pat. No. 5,035,144 discloses frequency broadband measurement of thecharacteristics of acoustic waves. Propagating acoustic waves aredetected by two different broadband receivers at first and secondlocations separated by a distance L. The data analysis for this methodinvolves detailed comparisons between group and phase velocities of thedata using different amplifiers and narrow band filtering of the signal.

U.S. Pat. No. 5,604,592 discloses a laser ultrasonics-based materialanalysis system and method using matched filter processing. The systemuses a diode laser for detection. Generation and detection of ultrasoundis done at different points. The system relies on Time of Flight (TOF)detection which requires generation and detection at separate pointssince the basis of the measurement is the time it takes for theultrasonic energy to travel between the two points. The waveshape of thetime varying ultrasonic signal is acquired with a matched filter,processed and basically compared to a library of similar signals.

U.S. Pat. No. 5,615,675 discloses a method and system for 3-D acousticmicroscopy using short pulse excitation and a 3-D acoustic microscopefor use therein.

U.S. Pat. No. 5,305,239 discloses ultrasonic non-destructive evaluationof thin specimens. The method involves data analysis for thin specimens,where “thin” is defined as less than or equal to the wave-length of theinspecting acoustic wave. Analysis is demonstrated with a Fast FourierTransform (FFT). An important aspect of an FFT is that it can onlyproduce discrete frequency results determined by the number of pointstaken and data rate used.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a method and system forquickly processing measurement signals to obtain a value for a physicalparameter in a measurement system in which time-varying physical signalscontaining frequency information related to the physical parameter of anobject are measured to obtain the measurement signals.

Another object of the present invention is to provide a method andsystem for processing measurement signals to obtain a value for aphysical parameter in a measurement system in which time-varyingphysical signals containing frequency information related to thephysical parameter of an object are measured to obtain the measurementsignals, wherein a simple procedure need be performed to measure thephysical parameter and wherein no environmental calibration procedureneed be performed.

Still another object of the present invention is to provide a method andsystem for processing measurement signals to obtain a value for aphysical parameter in a measurement system in which time-varyingphysical signals containing frequency information related to thephysical parameter of an object are measured to obtain the measurementsignals. The physical parameter may be thickness, acoustic impedance,signal transit time, density, speed of sound, attenuation or viscosityof the object which may be a static or dynamic film layer formed on asubstrate layer.

Yet, still another object of the present invention is to provide anon-calibrating method and system for processing measurement signals toobtain a value for a physical parameter in a measurement system in whichtime-varying physical signals containing frequency information relatedto the physical parameter of an object are measured to obtain themeasurement signals. The physical parameter may change in value overtime from an initial value to a final value. The frequency informationis related to propagation of waves in the object and the frequencyinformation is processed with a model of the propagation of the waves inthe object.

In carrying out the above objects and other objects of the presentinvention in a measurement system wherein time-varying physical signalscontaining frequency information related to a physical parameter of anobject are measured to obtain corresponding time-varying measurementsignals, a method is provided for processing the measurement signals toobtain a value for the physical parameter. The method includes the stepof extracting the frequency information from the measurement signals.The frequency information includes at least one desired frequency. Themethod also includes the step of converting the frequency information toa value for the physical parameter.

Further in carrying out the above objects and other objects of thepresent invention in a measurement system wherein time-varying physicalsignals containing frequency information related to a physical parameterof an object are measured to obtain corresponding time-varyingmeasurement signals, a system is provided for processing the measurementsignals to obtain a value for the physical parameter. The systemincludes means for extracting the frequency information from themeasurement signals. The frequency information includes at least onedesired frequency. The system also includes means for converting thefrequency information to a value for the physical parameter.

Preferably, the frequency information includes a decay rate and anamplitude for the at least one desired frequency.

The object may be a static film which is a cured layer formed on asubstrate. The physical parameter may be thickness of the layer.

The object may be a dynamic film having a physical parameter whichchanges in value over time. The dynamic film may be a wet or dehydratedlayer formed on a substrate wherein the physical parameter is thicknessof the layer.

The physical signals may be electromagnetic signals such as coherentlight signals wherein the coherent light signals are modulated coherentlight signals and wherein the modulated coherent light signals aremodulated based on the frequency information.

Where the physical parameter changes in value over time from an initialvalue to a final value, the step of converting includes the step ofpredicting the final value from the initial value.

Where the physical parameter changes in value over time from the initialvalue to an intermediate value and then to the final value, the step ofpredicting includes the step of first predicting the intermediate valuefrom the initial value and then predicting the final value from theintermediate value.

The object may be a curable film and the physical parameter may be filmthickness and wherein the initial value is wet film thickness, theintermediate value is uncured film thickness and the final value iscured film thickness.

The frequency information may be related to propagation of waves in theobject where the step of predicting includes the step of processing thefrequency information with a model of the propagation of the waves inthe object.

The measurement signals are preferably discrete-time signals wherein thestep of extracting includes the step of transforming the discrete-timesignals to a Z-domain and wherein the frequency information is containedin at least one zero or pole in the Z-domain.

Preferably, the frequency information includes an amplitude and a decayrate for the at least one frequency wherein the step of extractingfurther includes the step of converting at least one zero or pole in theZ-domain to the at least one frequency and its decay rate.

In the disclosed embodiment, the measurement signals are ultrasonicelectrical signals wherein the frequency information is related topropagation of longitudinal ultrasonic waves in the object.

The above objects and other objects, features, and advantages of thepresent invention are readily apparent from the following detaileddescription of the best mode for carrying out the invention when takenin connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view illustrating a typical automotive coatingprofile;

FIG. 2 is a schematic view of a simplified measuring system with atwo-fiber laser launch system of FIG. 5 and constructed in accordancewith the present invention;

FIG. 3 is a schematic view of a three-fiber sensor head constructed inaccordance with the present invention without its housing;

FIG. 4 is a schematic view of a two-fiber sensor head constructed inaccordance with the present invention;

FIG. 5 is a schematic view of a two-fiber laser launch systemconstructed in accordance with the present invention and utilized inFIG. 2;

FIG. 6 is a schematic view of a more complex system constructed inaccordance with the present invention with generation and detectionlasers and an interferometer of the system located in a laser roomremote from an automotive paint booth in which sensor heads of thesystem are located;

FIG. 7 is a schematic side elevational view of an automotive vehiclebody carried by a conveyor and a portion of a sensor arch having sensorheads constructed in accordance with the present invention;

FIG. 8 is a schematic top plan view of a plurality of sensor archespositioned at various locations within a paint booth;

FIG. 9 is a graph illustrating a laser ultrasonic signal obtained frommeasuring a wet green paint on a 1.0 mil E-Coat with a 1.6 mil primer;

FIG. 10 is a graph of the signal of FIG. 9 after transformed by adiscrete Fourier transform and which illustrates resonance frequenciesof the substrate and a paint film;

FIG. 11 is a set of graphs, each one of which is similar to the graph ofFIG. 10 and illustrating how paint peak resonant frequencies change withvarying wet paint thickness;

FIG. 12 is a graph illustrating how a calibration curve could begenerated from LU measured values of a wet white solvent base coat; and

FIG. 13 is a schematic block diagram flow chart illustrating aprocessing method and system which focuses on how raw ultrasonic signalsand/or data are analyzed.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring now to FIG. 2, there is illustrated a schematic view of asimplified system constructed in accordance with the present invention,generally indicated at 22. The system includes a generation laser 24, adetection laser 26, and an interferometer 28.

The generation laser 24 is preferably a Nd:YAG laser with an added fixedOPO having a 1570 nm wave-length which provides <10 mJ/pulse at themeasured article. The laser 24 produces a very short pulse (˜10 ns) thatis used to generate the ultrasound in a thin liquid or solid film suchas paint formed on the article 30. The absorption of this laser's lightpulse energy causes a temperature rise in the film (certainly <5° C.,probably less than 1° C.) which, in turn, produces an essentiallyinstantaneously generated density gradient in the material. This densitygradient produces ultrasound. (This type of ultrasound generation isreferred to as thermoelastic generation.) Thus, the short laser pulse isanalogous to a quick hammer strike to a bell thereby generating sound.

For wet films, a second method of ultrasound generation is also present.The energy in the pulsed laser 24 is very small, considerably too smallto affect the solid materials in the paint, however it will cause anextremely small portion of solvent (μL) on the film surface to bequickly evaporated. The movement of this solvent mass away from the filmproduces a force in the opposite direction (i.e., into the film) whichis very efficient at generating ultrasound. This ultrasound generationmethod is referred to as ablative generation, which typically damagesthe surface of the article inspected. The energies used for thisinvention will only ablate liquids, not solids, thus no damage occurs tothe solid film material.

The detection laser 26 is preferably a Nd:YAG laser having a 1064 or 532nm wavelength, >2 MHz line-width and provides ≦500 mW of power at thearticle inspected. The laser 26 is a nominally continuous (wave, or CW)laser which is used to detect the minute motions (<1 nm) of the samplesurface due to the ultrasound. The laser 26 can be thought of asproducing a very long pulse especially when compared to the length ofthe pulse produced by the laser 24.

The laser 26 has a very narrow linewidth and thus it is possible torecord the ultrasonic surface motions by monitoring the laser frequencyas it is Doppler shifted by the ultrasonic motions. The resultingdetection laser light pulse reflected off the article 30 is coupled intothe interferometer 28 via an optical fiber 41. The interferometer 28strips away and records the modulations in this laser light pulse linefrequency. The frequency of the film resonance is directly related toits thickness, with a thicker film having a slower resonance, again likea bell.

The interferometer 28 is preferably a confocal Fabry-Perot typeinterferometer constructed generally in accordance with the teachings ofthe above-noted U.S. Pat. No. 5,137,361.

The system 22 also includes a first optical fiber 32 for transmittingthe first pulse generated by the generation laser 24 therethrough to asensor head, generally indicated at 34, which is shown positioned withina spray booth 36 in which the article 30 is located.

The system 22 also includes a second optical fiber 38 for transmitting asecond light pulse generated by the detection laser 26 therethroughafter striking a reflective element or prism 107 in a system 100 asillustrated in FIG. 5 which directs the second light pulse into theoptical fiber 38.

In general, the sensor head 34 directs the first light pulse appearingon the optical fiber 32 at a sensing station within the paint booth 36toward a first spot 42 along light signal path 44 on a surface of thefilm of the article 30 to generate an ultrasonic wave such as alongitudinal ultrasonic wave in the film which, in turn, causesultrasonic motion of the surface of the film without damaging the filmor the rest of the article 30.

In general, the sensor head 34 also directs the second pulse of lighttransmitted through the second optical fiber 38 at the sensing stationtoward a second spot 46 which is coincident and overlaps the first spot42 along a light signal path 48 to obtain a reflected pulse of lightwhich returns to the sensor head 34 along a path back to the sensorhead. The limits of such a path are indicated at 50 in FIG. 2. Thereflected pulse of light is modulated based on the ultrasonic motion ofthe surface of the film, as is well known in the art.

Referring to FIGS. 2 and 5, the sensor head 34 transmits the reflectedpulse of light from the sensing station to the optical fiber 38 and thenout of the fiber toward a lens 112 of FIG. 5. This light is coupled intothe fiber 41 by the lens 112 therethrough so that it is received by theinterferometer 28 along the optical fiber 41. The interferometer 28detects the reflected pulse of light to obtain a correspondingultrasonic electrical signal such as the one illustrated in FIG. 9.

A three-fiber system may be used instead of the two-fiber system of FIG.2 to eliminate the block 100. However, an extra fiber is needed asillustrated at 76 in FIG. 3.

As illustrated in the embodiment of FIG. 6, the interferometer 28 iscoupled to a computer 50 to process the ultrasonic electrical signalprovided by the interferometer 28 to obtain a physical property signalsuch as a thickness signal which represents the thickness of the film orsubstrate of the multilayer article 30. In general, the computer 50 isprogrammed to initially digitize the ultrasonic electrical signal toobtain a discrete-time signal and then, by applying a Z-transformthereto, to obtain the resonance frequencies in the ultrasonic signal.The resonant frequencies obtained from the ultrasonic signal in FIG. 9are illustrated in FIG. 10. These frequencies in FIG. 10 were obtainedby a Fourier transform as opposed to a Z-transform for this illustrativeexample due only to the ease of graphing the output of a Fouriertransform. The actual method to extract the resonant frequencies is witha Z-transform and then the computer 50 processes the resonancefrequencies to obtain the thickness signal as described in greaterdetail hereinbelow.

Referring now to FIG. 3, there is illustrated one embodiment of a sensorhead, generally indicated at 52 and constructed in accordance with thepresent invention. The sensor head 52 typically includes a supporthousing (which housing is not shown in FIG. 3 for simplicity). Thesensor head 52 receives the first pulse of light from a coupler 54formed on one end of the fiber 32 to provide an optical signal 56 whichis transmitted through a dichroic beam splitter 58.

The sensor head 52 also supports a coupler 60 which couples the opticalfiber 38 to the sensor head 52 to transmit a laser light signal 62 tothe beam splitter 58 which reflects the second pulse of light. A lens 64focuses the first and second pulses of light to a prism or mirror 66which, in turn, reflects the first and second pulses of light alonglight signal path 68 to the spots 42 and 46 on the article 30. Thus, thefirst and second pulses of light are directed toward the articlecollinearly.

The resulting reflected pulse of light travels along any path within thelimits set by path 70 to a lens 72 which, in turn, focuses the reflectedpulse of light to a coupler 74. The coupler 74 is coupled to acollection fiber 76 which returns the reflected pulse of light to theinterferometer 28 thereby eliminating the necessity of having the system100.

Referring now to FIG. 4, there is illustrated a second embodiment of asensor head, generally indicated at 78. The sensor head 78 may beutilized in the system 22 since optical fiber 38 serves not only as adelivery fiber but also as a collection fiber.

The sensor head 78 includes a housing 80 for housing optical componentsof the sensor head therein. A typical standoff between the housing 80and the article 30 is 150 mm but can be widely varied. The sensor head78 includes a dichroic beam splitter 82 supported within the housing 80to transmit the first pulse of light generated by the generation laser24 appearing along path 84 as emitted from a coupler 86 which couplesthe optical fiber 32 to the housing 80 of the sensor head 78.

The beam splitter 82 also reflects the second pulse of light from theoptical fiber 38 through a coupler 88 along a path 90 so that theresulting first and second pulses of light are collinear within thesensor head 78 along a path 92 within the housing 80.

The sensor head 78 also includes a lens 94 for imaging the first andsecond pulses of light along a path 96 to the spots 42 and 46,respectively, on the film layer of the article 30. In turn, a reflectedpulse of light travels along any path within the limits set by path 96through the lens 94, travels along any path within the limits set bypath 92, is reflected by the beam splitter 82 to travel along any pathwithin the limits set by the path 90 back to the coupler 88 and backthrough the optical fiber 38 to the optical system 100 and to theinterferometer 28 through the fiber 41.

Referring again to FIG. 5, there is illustrated a schematic view of atwo-fiber laser launch system for the second pulse of light source. Ingeneral, the laser launch system 100 illustrates in detail how thesecond pulse of light is transmitted to the optical fiber 38 as well ashow the reflected pulse of light is transmitted from the optical fiber38 to the optical fiber 41 and then to the interferometer 28.

The system 100 includes a shutter 102 which allows a portion of thesecond pulse of light to pass therethrough along a path 104 to afocusing lens 106 which focuses the second pulse of light to a mirror orprism 107 which, in turn, directs the second pulse of light to a coupler108 which couples the second pulse of light to the optical fiber 38.

The reflected pulse of light is transmitted by the optical fiber 38 tothe coupler 108 and, after being emitted therefrom, travels along thepath 110 to the condenser lens 112 for focusing to the optical fiber 41by means of a coupler 114.

Referring now to FIG. 6, there is illustrated a more complex system,generally indicated at 120, also constructed in accordance with thepresent invention. The generation laser 24, the detection laser 26 andthe interferometer 28 of the system are located in a laser room 122which is remote from a paint booth 124 in which a plurality of sensorheads, such as the sensor head 34, are located at a plurality of sensorstations 130.

The system 120 includes multiplexing and demultiplexing elements 126 formultiplexing or directing the first and second pulses of light generatedby the generation laser 24 and the detection laser 26 into first andsecond pluralities of beams of light and for demultiplexing orcollecting the reflected pulses of light for detection by theinterferometer 28. Optical fiber bundles 128 extend between the room 122and local controllers 129 located near the paint booth 124 adjacenttheir respective sensor stations 130. The fiber bundles 128 providepaths for the first and second plurality of beams of coherent light andthe reflected pulses of light between the two areas. Each localcontroller 129 includes a computer for controlling multiplexing elements(not shown) for multiplexing or directing the first and second pulses oflight generated by the generation laser 24 and the detection laser 26and demultiplexers (not shown) for demultiplexing or collecting thereflected light pulses for ultimate use by the interferometer 28.

In this manner, only a few number of optical fibers need be connectedbetween the laser room 122 and the local controllers 129 which typicallywill be widely separated. A larger number of optical fibers 131 whichextend from the local controllers 129 to the plurality of sensor heads,such as sensor head 34, are of a much shorter length, thus reducing thetotal amount of optical fiber required. In systems with a few number ofsensor heads, the local controller multiplexer can be omitted.

In the embodiment of FIG. 6, multiplexing is utilized to take multiplemeasurements with the above components. Multiplexing both light sources24 and 26 and the reflected light pulses from the car body surfacescouple the light beams into the fiber optic cables 128. The lightsources 24 and 26 and the interferometer 28 are located remotely fromautomotive body assemblies 136.

With the use of acousto-optic (AO) cells and/or reflective optics ongalvanometers and/or translating fiber optical switches (or any form ofoptical switches), pulses from the light sources 24 and 26 can bedirected into a specified fiber of a large set of fibers. In conjunctionwith directing pulses from the light sources 24 and 26 into differentfibers, the output from the fiber which collects the reflected lightfrom the film surface is directed to the interferometer 28 for recordingand processing.

The fibers 131 are positioned to make measurements at the desiredmultiple remote positions at the sensor stations 130. The second lightsource 26 and the light reflected from the film of the article areeither carried on separate fibers or combined into a single fiber with abeam splitter or similar optic.

In this manner, the film build measurement of many different positionswith the same light sources and interferometer is achieved.

As illustrated in FIGS. 6 and 8, the article may be an automotiveassembly 136 of metal parts which moves relative to arches 142 of sensorheads 34 of the system. In such a system, position signals generated byan encoder and limit switches (not specifically shown but located withinthe local controllers 129) coupled to the moving assembly 136 through acarriage 134 are processed together with the measurements at thecomputer 50 to locate those areas of the film which are either too thinor too thick.

The method and system may be utilized with a robot controller 138 whichcontrols a robot 140 to spray coat a surface of the assembly 136 at thelocation of the thin film. Another method would utilize the thicknesssignals as a closed loop feedback control to adjust some parameter(s)(e.g. paint flow control) of the process.

In the example illustrated in FIG. 6, each optical fiber bundle 128preferably includes two optical fibers to service each local controller129. Each optical fiber bundle 131 preferably includes eighteen opticalfibers to service the nine total sensor heads 34 positioned at eachsensing station 130 within the paint booth 124.

The computer 50 operates as a data collection and analysis device. Aseparate computer system controller 141 serves as a controller forcontrolling operation of the generation laser 24, the detection laser26, the interferometer 28, and the multiplexing and demultiplexingelements 126. The system controller 141 includes input/output circuitsnot only for control purposes but also to allow the separate controller141 to communicate with either the limit switches and the encoder withinthe controllers 129 directly or, preferably, with other computers of thelocal controllers 129 which directly monitor these signals.

The encoders within the controllers 129 are coupled to an assembly line133 which, in turn, moves carriages 134 which support the automotivebody assemblies 136 as illustrated in FIG. 7.

The sensors shown in FIG. 7 may be fixed or contain rotation componentsto allow the sensors to remain pointed basically at the normals to thearticle.

The input/output circuits in the local controllers 129 allow itscomputer to communicate with the encoder(s) which generates a positionsignal representative of position of each carriage 134. Preferably, eachencoder is an optical incremental encoder mounted to a return wheelabout which a chain drive of the assembly line 133 moves. The localcontrollers 129 know when to look at the position signals provided bytheir encoders through the use of their limit switches which generatesignal inputs to the input/output circuits of the separate computer inthe laser room when the carriages 134 holding the assemblies 136 reachpredetermined positions within their sensor stations 130.

The data analysis computer 50 is coupled to a computer 137 whichreceives data from the data analysis computer 50 so that the computer137 can locate a surface defect in the film on the body assembly 136.The second computer 137 communicates with the computer 50 over a datalink 139 and which is located outside the room 122 to perform thesignal/data processing necessary to obtain the thickness whichrepresents the thickness of the film or the substrate as describedhereinbelow. There will be one networked data link between all thecomputers wherever they are located. obviously, to communicate among thecomputers one could install a LAN.

A signal is sent by the system controller 141 through its input/outputcircuits to the robot controller 138 which, in turn, generates a controlsignal based on location of the surface defect in the film on theassembly 136. The control signal from the robot controller 138 is usedby the robot 140 which is movable to a surface coating position tofurther coat the surface of the layer of the assembly 136.

Referring now to FIG. 7, there is illustrated a sensor head arch,generally indicated at 142, which includes a plurality of sensor heads34 mounted on vertically and horizontally extending beams 144 along thepath of the automotive assemblies 136 so that measurement readings canbe taken at various spots such as spots 146 along the car body assembly136. These sensors may be fixed as shown or contain rotation componentsto keep the sensor, either individually or in groups, pointed basicallynormal to the article at each inspection point 146.

Referring now to FIG. 8, there is illustrated a top plan view of aplurality of sensor arches such as the sensor arch 142 through whichautomotive car body assemblies 136 travel within a paint spray booth148. The laser room 122 contains the generation laser 24, the detectionlaser 26, the interferometer 28, the multiplexing/demultiplexingelements 126, the computer 50, and the separate computerized systemcontroller 141. Optical fiber bundles 128 transmit multiplexed laserlight signals therethrough to either various local controllers 129 andthen on to the sensor stations 130 in the booth 148 or directly to thesensor stations 130 themselves.

Referring now to FIG. 11, there is illustrated a set of graphs, each oneof which is similar to the graph of FIG. 10 and which illustrate how theresonant paint frequencies change with varying wet paint thickness.

FIG. 12 is a graph illustrating how a curve has been generated from LUmeasured values of wet white solvent base coat which calibration curvemay be stored within the computer 50 for data analysis. Preferably, thedata analysis computer 50 passes the resonant frequency signal of FIG.10, along with previous measurements made on the film or substrate andhence stored in the computer 50, into a model also stored in thecomputer 50 to determine film build of the film or the substrate on theassembly 136 as described in greater detail hereinbelow.

SUMMARY OF DATA ANALYSIS

In brief, there are three main components to the data analysis of themethod and system of the present invention: signal processing; signalmodeling; and wet-film to cured-film prediction.

For the particular case of laser-based ultrasonics, the method andsystem operate in accordance with the block diagram flow chart of FIG.13.

The flow chart of FIG. 13 is an example of the process involved in a wetpaint measurement. Briefly, the programmed computers 50 and 137transform the raw ultrasound signals or data at block 182 from theinterferometer 28 into amplitudes, frequencies, and decay rates afterprocessing at block 184. The frequencies measured are used in a model(physical model or calibration model) to yield a thickness measurementas indicated at block 186.

In the case of automotive coatings, one assumes the measurement ofmultiple plane-layered systems. The layers can be described as:

Substrate layer: usually steel, aluminum, plastic, or composite Staticfilm layer: usually cured paint, pri- mer, e-coat, clearcoat, phosphateDynamic film layer: usually wet or dehydrated paint, primer, clearcoat,e-coat, etc. Thickness and other physical prop- erties, changing withtime.

The method and system can be utilized to measure static and dynamicfilms.

There are several methods in which one can convert frequency tothickness. One can use straight calibration to convert frequency todried film thickness. The main disadvantages to calibrating dynamicfilms are the inclusion of extra variables. Some of these would be:

elapsed time of measurement from time of spray

temperature

humidity

preparation of paint

atomization pressure

fan patterning

paint composition

These effects may be impossible to quantify accurately.

In essence, a film loses base material via evaporation. The method andsystem of the present invention measure the amount of base and theamount of solids at the instant of measurement. The method and systemhave no need to include any of the aforementioned environmentalvariables that affect the wet film.

Signal Processing of Block 184

The invention models ultrasound as the summation of M decayingsinusoids. The modeling process is: find frequencies and decay ratesfrom raw data; and perform harmonic analysis of raw data using theseresults.

Find Frequencies and Decay Rates from Raw Data

One measures frequencies and decay rates from raw ultrasound data orsignals by pole-zero modeling. Specifically, the ultrasound signals onereceives can be modeled as exponentially decaying sinusoids. Thisproblem was first solved by Prony in 1795, and the basic mathematics aresubstantially identical to what one uses today. Only the computation ofthe math is modernized. Basically, a decaying complex sinusoid forms apole in the Z-transform domain. However, only frequency and decay rateinformation are contained in that pole as discussed by Oppenheim andSchafer in their book “Discrete-Time Signal Processing”, Prentice Hall,1989:

y(n)=Ae ^((−α+j2πf)n) u[n]<=>A(1−e ^((−α+j2πf)) z ⁻¹)⁻¹

where A is the amplitude of the signal, α is the decay rate, f isfrequency, and n is the discrete-time index.

By converting the problem of finding poles to a problem of findingzeros, the algorithm becomes:

Least-squares fit a linear prediction filter to the poles from raw data,i.e. transform signal to z-domain.

Find the zeros of the above filter in the z-domain.

Convert zeros to frequencies and decay rates.

Where:

L=size (order) of filter;

M=number of decaying sinusoidal signals in the raw data-in general M<L;and

N=number of raw data points to transform.

a. Least Squares Fit a Linear Prediction Filter to the Poles from RawData

From Prony's method, one solves the following equations to find thefilter: $A = \begin{bmatrix}{y^{*}(1)} & {y^{*}(2)} & \cdots & {y^{*}(L)} \\{y^{*}(2)} & {y^{*}(3)} & \cdots & {y^{*}( {L + 1} )} \\\vdots & \vdots & \quad & \vdots \\{y^{*}( {N - L} )} & {y^{*}( {N - L + 1} )} & \cdots & {y^{*}( {N - 1} )}\end{bmatrix}$ b = [b(1), b(2), …  , b(L)]^(T)

A

b=h

h=[−y*(0),−y*(1), . . . ,−y*(N−L−1)]^(T)

L=size of filter

N=number of raw data points to transform

y* is the complex conjugate of the data.

The above equation is very difficult to solve not only because ofnoisiness in y, but also because L>M. Essentially, two (or more) rows inthe matrix can become equal and cause a zero to appear in adenominator—one says that the problem is poorly conditioned orill-conditioned.

In laser ultrasonics of the present invention, the SNR rangesapproximately from 0 to 40 dB, i.e. low to moderate SNR. Moreimportantly, the number of sinusoids dynamically changes with the filmlayer system being measured. Therefore, one needs a robust method toextract the filter from the noisy data.

The SVD, or Singular Value Decomposition method, works quite well on theabove equations given the data laser ultrasound produces. The SVDmethod, as applied to the decaying sinusoid problem, was first describedby Kumaresan and Tufts in 1983 and is often called the KT method.

Basically, one solves the filter equation using SVD. With SVD, one canuse a filter whose order is larger than the number of signals oneexpects to receive. Increasing the filter size causes A to becomesingular. An intermediate solution then truncates the final solution toapproximate the number of signals. This improves the accuracy of the fitto the pole locations.

Presently, however, there is no need to truncate the SVD to obtaindesired results for frequency precision. Truncation often destroyed thedetectability of important signals (like low amplitude metal signals).Instead, “important” or desired signals are identified by amplitudes andknowledge of the film layer system.

b. Find the Poles of the Filter

The zeros of B(x) contain M signal zeros and L-M extraneous (or noise)zeros. The frequency/decay rate information is extracted by rooting thefilter polynomial B(x). For example, consider a one-signal system:

B(x)=1−e ^((−α+j2πf)) x=0<=>X=e ^((−α+j2πf))

B(z) is changed to B(x) to emphasize that the problem is changed fromfinding poles to finding zeros. Secondly, the signal zeros will havepositive decay rates (for exponentially damped signals) while the noisezeros will have negative decay rates. This is because noise level istheoretically constant (i.e. non-decaying). Finally, for zero decaysignals, noise can “push” the measured decay rate to a negative value.

Because of the fairly large order of polynomial, one needs a very robustmethod of extracting the poles from the filter. Iterative methods areslow and generally fail for large polynomials. An eigenvalue method isused to perform this calculation.

To find eigenvalues of a matrix, one performs the operation:

det[W−xI]=0

where det[ ] is the determinant of the matrix W−xI. The problem is setupusing the filter coefficients from B(x) in a companion matrix:${B(x)} = {{\det \lbrack {W - {xI}} \rbrack} = {{\sum\limits_{i = 0}^{L}\quad {{b(i)}x^{i}}} = 0}}$$W = \begin{bmatrix}{- \frac{b( {L - 1} )}{b(L)}} & {- \frac{b( {L - 2} )}{b(L)}} & \cdots & {- \frac{b(1)}{b(L)}} & {- \frac{b(0)}{b(L)}} \\1 & 0 & \cdots & 0 & 0 \\0 & 1 & \cdots & 0 & 0 \\\vdots & \vdots & \quad & \vdots & \vdots \\0 & 0 & \cdots & 1 & 0\end{bmatrix}$

Then, one can use basically the same theory (and mathematics) involvedin SVD to find the eigen-values of the new matrix. Specifically, a QRmethod is used to estimate the eigenvalues. Specifics of how to computethe QR decomposition are easily well known as SVD.

c. Convert from Roots to Frequencies and Decay Rates

The signal zeros are sorted from the noise zeros by ignoring all |z|<cwhere for now c=1.000000. This value may be changed to a number like0.980000 because sometimes the metal peaks' signal zeros are pushedinside |z|<1 by noise (these generally lie at about 0.9995 or 0.995).

To determine frequency f and decay α, one uses the following:

f=a tan(z _(i) /zr)/2π

α=−log(|z|)

Perform Harmonic Analysis of Block 184

In order to obtain amplitudes, one simply performs a harmonic dataanalysis using the frequencies and decay rates obtained above.Essentially, one performs a general linear least squares fit to the rawdata: $K = \begin{bmatrix}{\exp ( {s_{1}o} )} & {\exp ( {s_{2}0} )} & \cdots & {\exp ( {s_{L}0} )} \\{\exp ( {s_{1}1} )} & {\exp ( {s_{2}1} )} & \cdots & {\exp ( {s_{L}1} )} \\\vdots & \vdots & \quad & \vdots \\{\exp ( {s_{1}( {N - 1} )} )} & {\exp ( {s_{2}( {N - 1} )} )} & \cdots & {\exp ( {s_{L}( {N - 1} )} )}\end{bmatrix}$

Ka=y

a=[a₁,a₂, . . . ,a_(L)]^(T)

y=[y(0),y(1), . . . ,y(N−1)]^(T).

These equations are not ill-conditioned and are thus easy to solve bygeneral linear least squares. Specifically, a simple Gauss-Jordantechnique is used to invert K. This technique is also very well knownand specifics of computation will not be discussed further.

Signal Modeling of Block 186

Modeling of the propagation of ultrasound in the layers is important toany non-calibrating measurement, as described herein. The system ismodeled as a compressional wave traversing through plane layers.

Given enough information (i.e. from block 188) and enough signal (i.e.from block 184), one can find (true) wet thickness. Additionally, onecan find speed of sound, density, and possibly viscosity andattenuation. The acoustic impedance of a material is the product ofspeed of sound and density:

Z=ρc

Acoustic impedance controls how a wave is transmitted/reflected at aboundary (i.e. free, rigid, or other reflection) and how the “paint”frequencies interact with “metal” frequencies (and vice versa).Thickness and speed of sound determine how quickly the wave propagatesthrough a layer. Attenuation describes how much energy the wave loses(to heat or other) as it propagates through the layer. Given the modelof block 186, as well as good data from block 184, one can solve for anyof speed of sound, thickness, density, and/or attenuation usingoptimization techniques.

The resonance frequency model of block 186 is used to obtain thickness,speed of sound, and density information. Consider a lossless singlelayer film on a lossless steel substrate. The model for frequencyresonance for this particular system is:${{Z_{p}{\tan ( {2\pi \quad f\frac{d_{p}}{c_{p}}} )}} + {Z_{s}{\tan ( {2\pi \quad f\frac{d_{s}}{c_{s}}} )}}} = {0 = {Q( {d,c,\rho,f} )}}$

where f is any resonant frequency (paint or metal), d is thickness, c isspeed of sound, subscript p refers to paint layer qualities, andsubscript s refers to steel substrate qualities.

This equation can be solved numerically. Specifically, one minimizesQ(d,c,ρ,f) for desired variables/parameters/data. However, there aremany ways to perform the minimization. For example, since one knows thevarious properties of the steel, one minimizes the following:${{\frac{Z_{p}}{Z_{s}}{\tan ( {2\pi \quad f_{i}\frac{d_{p}}{c_{p}}} )}} + {\tan ( {2\pi \quad f_{i}\frac{d_{s}}{c_{s}}} )}} = {{Q( {{f_{i};z_{p}},\frac{d_{p}}{c_{p}}} )}/Z_{s}}$$ {{Min}_{simplex}{}{\sum\limits_{i}{{{Q^{2}( {{f_{i};z_{p}},\frac{d_{p}}{c_{p}}} )}/Z_{s}^{2}}{}}}}\Rightarrow z_{opt} ,( {d/c} )_{opt}$

where i=1, 2, . . . number of measured resonances. The ; symbolrepresents that z and d/c are parameters to be optimized while f_(i) isinput data. The minimization is performed using the well known simplexmethod, and will not be discussed in detail here.

Wet Prediction

The process to predict a cured film thickness from a wet film thicknessis a two-step process: Perform wet to uncured prediction of block 192;

estimate wet to uncured prediction factor from data of block 190;

calculate uncured thickness; and Perform uncured to baked or curedprediction of block 194.

Perform Wet to Uncured Prediction (Block 192)

Estimate Wet to Uncured Prediction Factor Via Laser-Based Ultrasound(Block 190)

Solving for the quantities such as d, c, and ρ in the wet layer isimportant. For the particular case of ultrasonic measurement, onemeasures impedance and one-way transit time of the wet layer—call themρ_(wet), c_(wet), and d_(wet), respectively. Density and speed of soundvary with particulate size and particulate concentration, as well assolvent properties. If one can measure impedance, one can then estimatepercent solids or particulate concentration—call percent solids R_(wet)(let R_(wet) be a pure ratio less than 1 and not a percent).Symbolically, one measures R_(wet) from one of ρ_(wet), c_(wet) orZ_(wet) as:

R _(wet) =f(ρ_(wet))

-or-

R _(wet) =f(c_(wet))

-or-

R _(wet) =f(Z_(wet))

-or-

R _(wet) =f(ρ_(wet) , c _(wet)).

One also uses this data to measure d_(wet).

The functionality of f ( ) is either derived or measured, depending onapplication, knowledge available, etc. Note that it is very possible tomeasure f ( ) using results from other techniques, say Time ResolvedInfrared radiometry (TRIR), as well as using this same process for wetprediction. See the next section for details.

Calculate Uncured Thickness (Block 192)

Once R_(wet) and d_(wet) (or even (Rxv)_(wet) and (d/v)_(wet) for thespecial case of this laser ultrasonic application) are estimated, one isready to perform wet prediction. The following wet film to dry filmthickness prediction conversion is independent of measurement method.

Percent solids or particulate concentration tells what the wet layerwill reduce to if all of the solvent is removed. The predictivethickness of the uncured but base-free paint is called d_(uncured).Mathematically, this is expressed as:

d _(uncured) =R _(wet) d _(wet)

or

d _(uncured)=(Rxv)_(wet)(d/v)_(wet).

As an example, if one measures 4 mils thick wet water-based(=d_(wet)=4.00 mil) at 75% solids (=R_(wet)=0.75), that means the wetlayer will reduce to 3 mils (=d_(uncured)=R_(wet)d_(wet)=0.75×4.00mil=3.00 mil).

Perform Uncured to Baked (i.e. Cured) Prediction (Block 194)

One must also know how the uncured wet layer chemically reacts to become“paint”. However, there is basically no way to predict how wet paintchemically reacts via ultrasound, thermal, image interferometry,microwave, millimeter wave, capacitance, etc., unless the reactionitself is monitored.

One measures the prediction in a laboratory or through knowledge of thechemical reaction. One method used with the present invention is tomeasure the prediction using density, as indicated at block 196. Thedensity of cured paint will be measured—call it ρ_(cured). The densityof uncured (and solvent- or water-free) paint will be measured—call itρ_(uncured). Because the paint has been applied to a surface, the areaof the uncured and cured paint is constant. Therefore, the uncured tocured paint prediction is:

d _(cured)ρ_(cured) =d _(uncured)ρ_(uncured).

One can then predict the final, baked or cured thickness, as indicatedat block 198.

It is possible that the above method can be used to measure wet glue todry glue thickness, as well as other properties of the glue. Moltencoatings, certain composites, etc. would also be measurable with themethod and system of the present invention.

Wet Film Prediction and Measurement

Determination of the Functionality of R_(wet)

There are several ways to determine the functionality of R_(wet). Firstis to use theory of the basic measurement technique. For example, onecould incorporate particle size, particle composition, particleconcentration, base composition, particle-base interaction, frequency,etc. into a physical model for f( ).

Another method to determine the functionality of R_(wet)=f( ) for agiven paint is calibration. As an example, consider measurement ofR_(wet)=f(c_(wet)) for black solvent-based paint. One can prepare manysamples of paint with various R_(wet) and measure the correspondingc_(wet). Then a curve can be fit in order to determineR_(wet)=f(c_(wet)).

While the best mode for carrying out the invention has been described indetail, those familiar with the art to which this invention relates willrecognize various alternative designs and embodiments for practicing theinvention as defined by the following claims.

What is claimed is:
 1. A method for determining properties of an objecthaving a surface that transitions from a substantially fluid state to asubstantially solid state, the method comprising: producing motions inthe surface of the object during the substantially fluid state withouttouching the fluid; collecting time-varying signals responsive to thesurface motions produced during the substantially fluid state; andcalculating a value for at least one substantially solid state propertyof the object based on the time-varying signals collected in thesubstantially fluid state.
 2. The method of claim 1, wherein the surfacemotions are produced by ultrasound.
 3. The method of claim 2, whereinthe surface motions are produced by the ultrasound without touching andwithout damaging either state of the surface.
 4. The method of claim 1,wherein the substantially fluid state is a saturated state characterizedby the presence of a solvent and the substantially solid state is anunsaturated state characterized by a substantial decrease in thepresence of the solvent.
 5. The method of claim 1, further comprisingdetermining a decay rate and a frequency for the time-varying signalscollected in the substantially fluid state by pole-zero modeling of thetime-varying signals, wherein pole-zero modeling comprises: modeling thetime-varying signals as exponentially decaying sinusoids; computingpoles of the modeled time-varying signals; least-squares fitting alinear prediction filter for the poles; determining zeros for the filterin the z-domain; and converting the zeros to the decay rate and thefrequency.
 6. The method of claim 5, wherein the filter is determinedusing a Prony's method.
 7. The method of claim 6, wherein the Prony'smethod is solved using Singular Value Decomposition.
 8. The method ofclaim 5, wherein the zeros for the filter are determined by a eigenvaluemethod.
 9. The method of claim 5, wherein converting the zeros to thedecay rate and the frequency includes sorting out noise zeros.
 10. Themethod of claim 5, further comprising determining an amplitude for thetime-varying signally collected in the substantially fluid state byharmonic data analysis of the decay rate and the frequency.
 11. Themethod of claim 1, further comprising determining a resonance frequencyfor the time-varying signals collected in the substantially fluid state.12. The method of claim 11, further comprising determining thickness,speed of sound, and density based on the resonance frequency.
 13. Themethod of claim 11, wherein determining the resonance frequency includesmodeling a propagation of ultrasound in the surface as a compressionalwave traversing through the substantially fluid state of the surface.14. The method of claim 1, wherein the calculated value is a thicknessof the object in the substantially solid state.
 15. The method of claim14, wherein the thickness comprises: calculating a thickness of theobject in the substantially fluid state; determining a prediction factorfor a transition of the object from the substantially fluid state to thesubstantially solid state; and calculating the thickness of the objectin the substantially solid state based on the prediction factor and thethickness of the object in the substantially fluid state.
 16. The methodof claim 15, wherein determining the prediction factor comprises:measuring impedance of the object in the substantially fluid state;estimating percent solids of the object in the substantially fluidstate; and calculating the prediction factor based on the measuredimpedance and the estimated percent solids.
 17. The method of claim 15,wherein determining the prediction factor is based on a physical model.18. The method of claim 15, wherein determining the prediction factor isbased on a calibration model.
 19. The method of claim 1, whereincalculating the value for at least one substantially solid stateproperty does not include an environmental calibration procedure. 20.The method of claim 1, further comprising: determining a desired valuefor the calculated property; comparing the calculated property value tothe desired property value; and producing a control signal thatrepresents the comparison of the calculated valve to the desired value.21. The method of claim 20 for a substrate and wherein the object is acoating, further comprising: providing a robot having a controller and ameans for applying the coating to the substrate, wherein the coatingproduces the surface that transitions from the substantially fluid stateto the substantially solid state; inputting the control signal to therobot; and controlling the robot based on the control signal, whereinthe application of the coating is controllable by the robot based on thecontrol signal.
 22. The method of claim 21, wherein the object and therobot are in an automotive assembly line.
 23. The method of claim 21,further comprising: inputting position signals to the robot relating tothe position of the surface, wherein the robot is movable to the surfaceposition in response to the position signal for further coating of thesubstrate.
 24. The method of claim 21, further comprising: producingmotions in the surfaces of a plurality of objects having a surface thattransitions from a substantially fluid state to a substantially solidstate; providing multiple robots having a controller and a means forapplying a coating to each substrate, wherein the coating produces thesurface that transitions from the substantially fluid state to thesubstantially solid state; inputting multiple control signals responsiveto each substrate to a computer; and providing a system controller forreceiving signals from the computer and selectively controlling eachrobot by producing individual control signals for each robot;controlling each robot according to the individual control signals. 25.An apparatus for determining wet and dry properties of a surface of anobject, the apparatus comprising: laser means for producing surfacemotions in the object without touching the object and time-varyingsignals responsive to the surface motions; a detection device formeasuring the time-varying signals; a processor for calculating at leastone wet property of the surface based on the time-varying signals topredict a dry property value of the surface; and a surface provider forproviding an enhanced dry property value if the predicted dry propertyvalue is unacceptable.
 26. A method of covering a substrate with a wetmaterial dryable to an appearance finish of predetermined thicknesswithout marring the appearance finish comprising: covering the substratewith an initial coating of wet material to an unknown thickness;exciting the initial coating thereon; projecting a reflectable laserbeam toward the initial coating; receiving the reflection of the laserbeam while the initial coating is still wet; and converting thereflection to a measurement signal indicative of the thickness of theinitial coating.
 27. The method of claim 26, including covering thesubstrate with an additional coating of wet material while the initialcoating is still wet and until the measurement signal indicates theappearance finish has the predetermined thickness.